January 2019’s topic of The Galleseum –Acrylic Math’s FREE monthly art newsletter– is about the relationship between art and math, which dates back to antiquity and spans to modern times. And, this is the corresponding Blog Post.
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An odd couple? Not really! The relationship between art and math dates back to antiquity and spans to modern times. In 4 BC, the Greek sculptor Polykleitos of Argos described the ideal mathematical proportions of the human body in a work titled the Kanon.   During the Renaissance, Leonardo da Vinci, the Italian genius, also described the ideal mathematical proportions of the human body in a drawing titled L’Uomo Vitruviano  (See Figure 1: The Vitruvian Man by Leonardo da Vinci. Public domain. )
And, in modern times, Piet Mondrian, the famous Dutch painter, used simple geometric elements in his work  (See Figure 2: Composition No. III by Piet Mondrian. Public domain. ).
The Golden R
The golden ratio is represented by the
Art cognoscenti have identified the use of the golden rectangle in design. For example, Samuel Obara of the Department of Mathematics of the University of Georgia recognized
Tessellations, from the Latin tessella (small square), are tilings of continuous shapes: Euclidean, organic, and three-dimensional.  Figure 5 (Penrose tiling. Public domain. ) displays an example of a tessellation.
Tesselations were used in ancient Rome and in the Islamic world, notably in the Alhambra, in Granada, Spain (See Figure 6: Tessellation, Alhambra, Seville, Spain. © 2007 Gruban. Reprinted with permission. ) In modern times, the renowned Dutch artist M.C. Escher use tessellations in his work. 
Fractals, from the Latin fractus (broken), are detailed patterns that endlessly repeat themselves at different scales. Fractals are characterized by self-similarity and non-integer dimensions.   Fractal geometry is rooted in the seminal works of Gottfried Leibniz, the
Myriad examples document the relationship between art and math. The three topics briefly presented herein -the golden ratio, tessellations, and fractals- are but “small cogs in the large wheel” of art and math.
 Mathematics and art. (2018). From Wikipedia. URL: https://en.wikipedia.org/wiki/Mathematics_and_art
 Polyclitus. (2018). From Encyclopedia Britannica. URL: https://www.britannica.com/biography/Polyclitus
 Vitruvian Man. (2018). From Wikipedia. URL: https://en.wikipedia.org/wiki/Vitruvian_Man
 Da Vince, L. (2018). Vitruvian Man. From Wikimedia Commons. URL: https://commons.wikimedia.org/wiki/File:Da_Vinci_Vitruve_Luc_Viatour.jpg
 Jaffe, H.L.C. (2018). Piet Mondrian. From Encyclopedia Britannica. URL: https://www.britannica.com/biography/Piet-Mondrian
 Mondrian, P. (1929). Composition No. III. From The Athenaeum. URL: https://www.the-athenaeum.org/art/detail.php?ID=85852
 Berry, B. (2017). What is the golden ratio? From Math Hacks. URL: https://medium.com/i-math/what-is-the-golden-ratio-d3cc17c8fefd
 Golden rectangle. (2018). From Wikipedia’s. URL: https://en.wikipedia.org/wiki/Golden_rectangle
 Golden Rectangle. (2018). From Wikimedia Commons. URL: https://commons.wikimedia.org/wiki/File:SimilarGoldenRectangles.svg
 Obara, S. (n.d.). Golden ratio in art and architecture. From The University of Georgia, URL: http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html
 Mondrian, P. (1030). Composition No. II. From Wikimedia Commons. URL: https://commons.wikimedia.org/wiki/File:Piet_Mondriaan,_1930_-_Mondrian_Composition_II_in_Red,_Blue,_and_Yellow.jpg
 Tessellation. (2018). From Wikipedia. URL: https://en.wikipedia.org/wiki/Tessellation
 Penrose tiling. (2009). From Wikimedia Commons. URL: https://commons.wikimedia.org/wiki/File:Penrose_Tiling_(P1_over_P3).svg
 Gruban. P. (2007). Tesselletion, Alhambra, Seville, Spain. From Wikimedia Commons. URL: https://commons.wikimedia.org/wiki/File:Tassellatura_alhambra.jpg
 Fractal. (2018). From Encyclopedia Britannica. URL: https://www.britannica.com/science/fractal
 What is a fractal? (n.d.) From Fractal Foundation. URL: https://fractalfoundation.org/fractivities/WhatIsaFractal-1pager.pdf
 Fractal. (2018). From Wikipedia.URL: https://en.wikipedia.org/wiki/Fractal